After reading much local forum
discussion on the general perception and subsequent
application of the Motor Thrust v Gross Lift
Off Weight ratio, CGN's Fridge made the following
comment to the forum membership:
"At the end of the day, I believe that a fairly
simple guideline has been molested into an ultra-simplistic
variance that fornicates with arbitrary values to produce
an inordinately overcomplicated field tool."
This was not received well by some of those in the
forum membership.
Read the salvaged forum thread here.
Fridge had this to say:
Oh My God... wait a moment, I'm not religious - Oh
My Porn Account! Where do I begin with this one? Actually,
I pretty much had an issue with this thread from the
time of it's initial posting. Too bad we can't read
it all SINCE POSTS HAVE BEEN DELETED! (Yeah, I'm still
hung up on that, just can't seem to see the thread for
the pussies).
What is it exactly
that we are talking about?
The ratio of one force compared to another. How much
force is moving the rocket up compared with how much
force is holding the rocket back. The thread title states
GLOW to Initial Thrust where it should have been stated
the other way around: Initial Thrust to GLOW as that
is the way the ratio values are always presented 5:1,
Thrust:Weight. Seems minor, I know, but if someone is
just learning then; less assumptions are made and less
confusion is had later on if terminology is correct
from the start.
Ideally, a safe model rocket flight is considered to
be one that goes straight up. The forces that act on
a rocket in flight are:
1. Thrust - provided by the motor
2. Weight - provided via the mass of all the bits
that make up the rocket
3. Lift - provided by the external surfaces
4. Drag - also provided by the external surfaces
Once the rocket leaves the launch rod (or whatever
system is being used) it relies on several things to
keep it on that vertical course. In model rockets, one
of the things often required for stability are fins
and the need for air to be moving around them fast enough.
This is terribly simplistic of course as there are several
disciplines of physics and maths devoted to the nitty
gritty of what happens in that short distance of translation
between not moving and leaving the end of the launch
rod into flight. The 5:1 ratio is supposed be a simple
verifying calc to ensure sufficient velocity at the
time of leaving the launch guide for a straight up flight
for a properly constructed rocket.
Why are we talking
about it?
Basically, the thread started with a reference to the
yanks using the 5:1 Thrust to Weight
ratio at their launches and that we, for safety's sake,
should adopt it over here. Not a bad premise, albeit
slightly lacking in information.
The NAR - National Assosiation of Rocketry only seem
to stipulate that you use certified motors and you use
them to the manufacturers recomendations. This would
then imply that if the manufacturer has listed a maximum
lift-off weight for that particular motor, then the
mass of the motor plus the mass of the rocket does not
exceed that stated value (Note the misuse of the term
weight here).
The TRA - Tripoli Rocketry Association has four conditions
to abide by regarding the motor choice:
1. The motor is currently certified
2. The total installed power does not exceed the limitations
of the field
3: The rocket can withstand the thrust produced by
the motor
4: The initial thrust will provide at least
a 5:1 thrust to weight ratio
view TRA's RSO guidelines here.
With condition 4, the guideline gives five examples
- three examples sir - three examples of how
the 5:1 can be verified:
1. Provide documentation showing the initial
thrust provided by the motor
2. Use the average thrust given that it will
always be at most equal to the initial thrust
5. Provide results from flight prediction software
that shows either:
a) thrust to weight > 5:1
b) initial accelaration > 5 g's
c) velocity at the end of the launch guide to be
> 45 feet/second
The PARC - Perth Advanced Rocket Club lists in their
Range Manual the following
five conditions - three conditions sir - three
conditions:
1. The motor being used must be an approved model
rocket motor
2. Provide a LWR greater than 4
5. Have a delay that will ensure safe recovery
view PARC's 1998 Range Manual here. (Well, it use to be there but they didn't like it being linked to by us.)
With condition 2, the PARC Range Manual describes LWR
as:
Lift to Weight ratio; the ratio between the
initial thrust of a motor and the mass of the model.
This definition is incorrect on many levels:
Lift is a force that is generated only once the
rocket is moving &;
Lift acts perpendicular to the direction of travel.
Either way, it's not included in the ratio.
Mass is a different quantity to weight and while
used in the calculation, is not a value in the ratio (Well, not without converting the Thrust value to kg at least).
The mass used is a combination of both the complete
model and the motor which is why it is most commonly
referred to as Gross Lift-Off Weight.
How to work it out
The Thrust to GLOW ratio is a dimensionless quantity
since is uses the same units for both values so the
units then cancel each other out.
Thrust, a force measured in Newtons
Weight, also a force measured in Newtons
The Initial Thrust values can be obtained from several
sources:
NAR
Motor Certification Page
TRA
Motor Certification Page
CAR
Motor Index
For the limp dicks, the Average Thust values can be
obtained from the motor designation and if applied using
the 5:1 calculation will result (usually) in a much
higher Initial Thrust to GLOW ratio.
The Gross Lift-Off Weight comes from the mass (m kg)
of the rocket in its ready to launch state i.e. Everything
loaded and ready to go - multiplied by the acceleration
due to gravity (g ms-2). GLOW =
m x g Newtons
The value for acceleration due to gravity (g) can be
worked out via this formula:
g = 9.80632 - LAT1 + LAT2 - ALT ms-2
where:
LAT1 = 0.02586 x cos 2ø
LAT2 = 0.00003 x cos 4ø
ALT = 0.00000293 x h
ø = degrees latitude
h = height in metres above sea level.
...Or you could just use 9.8 ms-2
Now all you need to do is compare the two values and
make sure that the Thrust is at least 5 times greater
(4 times for PARC) than the Weight.
i.e Fthrust > 5mg or, where g
= 9.8
Fthrust > 49m
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